I can only think that the Microsoft and 'Nokia' solutions were both in development in parallel, though why an executive didn't step in to cancel the launch of one or the other is rather strange. The Nokia HD-10 does have extra features, by way of the NFC-pairing coaster, but otherwise there's very similar Miracast functionality.
From the Microsoft blog post:
...Today we’re announcing the Microsoft Wireless Display Adapter, which connects to an HDTV, monitor, or projector and will let you easily share content from any Miracast-enabled device – including many PCs and Tablets running Windows 8.1. With the Wireless Display Adaptor, I don’t have to worry about getting everyone to huddle around a device. All the content I care about, along with audio, is easily shared on the big screen.
All you need to do is plug the USB end and HDMI end of the Microsoft Wireless Display Adapter into an HDTV, monitor or projector. Then select the right input on your TV, pair it with your laptop, tablet, or smartphone and you’ll be ready to go. Then just wirelessly project your screen from your Miracast-enabled device. It’s that simple. Depending on your device, you can have it mirror exactly what’s being shown on the screen of your device or extend its screen. Because the Microsoft Wireless Display Adapter uses Miracast technology, you’re not limited to certain apps or content streaming. It’ll show anything and everything from your device!
I was lucky to get my hands on a Microsoft Wireless Display Adapter to try out for myself.
...The other thing that is really slick is being able to open Office documents – like a PowerPoint slide deck – and have it shown on my HDTV through the Microsoft Wireless Display Adapter. This makes it a great tool for use at work – in a conference room – and not just at home. Remember, the Microsoft Wireless Display Adapter works with projectors and monitors too, so no more searching for the right, fitted adapter that plugs into your laptop every time you’re presenting.
You can also bring the Microsoft Wireless Display Adapter with you when you’re traveling and hook it up to the HDTV in your hotel room to play movies (and keep the kids entertained) or check out your photos from the day.
Of course, there may well be geographical reasons why the Microsoft and Nokia Miracast solutions co-exist. The Microsoft Wireless Display Adapter is available for preorder now in the U.S. and Canada and available in October. While the Nokia HD-10 is supposed to be available this month (anyone seen it yet?) in Europe.
Although these solutions handle video as well as screen sharing, it should be emphasised that, depending on the device (only the Windows Phones with the newer chipsets - like the 630, 930, 1520, etc. - are supported here), gaming may be a bit hit and miss because of latency issues, typical with Miracast streaming.
PS. Micracast is often compared to the likes of Google's cheaper Chromecast solution, though the latter is a) subsidised by Google, and b) works in a different way, with the control device simply directing the dongle to go off to the network to get its own content. This is more efficient, but is obviously more limited in what can appear on-screen.